Hypothesis testing for Markov chain Monte Carlo

Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are useful when one is interested in deciding whether the expected...

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Bibliographic Details
Published in:Statistics and computing 2016-11, Vol.26 (6), p.1281-1292
Main Authors: Gyori, Benjamin M., Paulin, Daniel
Format: Article
Language:English
Subjects:
Artificial Intelligence
Hypotheses
Hypothesis testing
Markov analysis
Markov chains
Mathematics and Statistics
Monte Carlo simulation
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:Testing between hypotheses, when independent sampling is possible, is a well developed subject. In this paper, we propose hypothesis tests that are applicable when the samples are obtained using Markov chain Monte Carlo. These tests are useful when one is interested in deciding whether the expected value of a certain quantity is above or below a given threshold. We show non-asymptotic error bounds and bounds on the expected number of samples for three types of tests, a fixed sample size test, a sequential test with indifference region, and a sequential test without indifference region. Our tests can lead to significant savings in sample size. We illustrate our results on an example of Bayesian parameter inference involving an ODE model of a biochemical pathway.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-015-9594-1